1) In a box there are 14 identical batteries. Two of the batteries are empty. You need two batteries for a remote contro

[answerhappygod]

1)
In a box there are 14 identical batteries. Two of the batteries
are empty. You need two batteries for a remote control and pull
randomly without backtracking from the box. The remote control only
works if both batteries work.
What is the probability that both batteries you have pulled, and
thus the remote control, work?
2)
Last autumn, a municipality carried out a registration of light
use among cyclists in the morning while it was still dark. Based on
this study, we have been given the following probabilities for a
random cyclist:
P (the cyclist has lights in front and behind) = 0.35,
P (the cyclist only has a light in front) = 0.21,
P (cyclist has only rear light) = 0.06.
The rest of the cyclists were completely without lights.
(a) What is the probability that a bicycle has a light in
front?
0.56
(b) What is the probability that a bicycle has a rear light?
0.41
(c) If you find out that a bicycle has a light in the
front, what is the probability that it also has a light in the
back?